Pollaczek polynomials and summability methods
type: Item
instance of: scholarly article
title: Pollaczek polynomials and summability methods
zbMATH Open document ID: 0703.33007
DOI: 10.1016/0022-247X(90)90365-M
author: Walter Van Assche
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Pollaczek polynomials satisfy a three-term recurrence formula for which the recurrence coefficients are rational functions of the degree n of the polynomial. They are important because they furnish an explicit example of orthogonal polynomials on [-1,1] for which the asymptotic theory of G. Szegö is not valid. Some Pollaczek polynomials are also important for the radial Coulomb problem in quantum mechanics. In both cases an asymptotic formula for the polynomials gives a lot of information. Such an asymptotic formula is usually obtained by using Darboux's method. The present paper gives an alternative approach based on regular transformations of sequences. The asymptotic formula holds whenever the variable is real and outside the oscillatory region [-1,1].
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 40C05
zbMATH DE Number: 4152834
zbMATH Keywords: Pollaczek polynomials
zbMATH Keywords: regular transformations
MaRDI profile type: Publication
cites work: Recurrence relations, continued fractions, and orthogonal polynomials
cites work: The attractive Coulomb potential polynomials
cites work: Q4170993
cites work: Q5788558
cites work: Q3327119
cites work: Orthogonal polynomials
cites work: Q5726007
cites work: Q5800910
cites work: Q5800911
cites work: Q5798212
cites work: Q5849060
cites work: Q5662429
cites work: Q5514782
cites work: On the Strong Law of Large Numbers and Related Results for Quasi-Stationary Sequences
cites work: On Certain Special Sets of Orthogonal Polynomials
full work available at URL: 0022-247x(90)90365-m
OpenAlex ID: W2035172022
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description: scientific article; zbMATH DE number 4152834